Lie algebras with the minimal condition on centralizer ideals (Q910842)

The authors develop the theory of Lie algebras with minimal condition on centralizer ideals. This class is not closed under extensions, quotients or taking of ideals. Abelian-by-finite Lie algebras always satisfy this condition. For semisimple Lie algebras satisfying this condition, maximal centralizer ideals are the same as minimal prime ideals and every centralizer ideal is the intersection of maximal centralizer ideals. The paper concludes with several open questions.